Related papers: Representing three-dimensional cross fields using …
An $n$-cross field is a locally-defined orthogonal coordinate system invariant with respect to the cubic symmetry group. Cross fields are finding wide-spread use in mesh generation, computer graphics, and materials science among many…
The classification of all fourth-order anisotropic tensor classes for classical linear elasticity is well known. In this article, we review the related problem of explicitly computing the dimension and the expressions of the elements…
Multipolar expansions are a foundational tool for describing basis functions in quantum mechanics, many-body polarization, and other distributions on the unit sphere. Progress on these topics is often held back by complicated and competing…
The analysis and visualization of tensor fields is a very challenging task. Besides the cases of zeroth- and first-order tensors, most techniques focus on symmetric second-order tensors. Only a few works concern totally symmetric tensors of…
This paper investigates the learning of 3rd-order tensors representing the semantics of transitive verbs. The meaning representations are part of a type-driven tensor-based semantic framework, from the newly emerging field of compositional…
In this paper we study finite dimensional algebras, in particular finite semifields, through their correspondence with nonsingular threefold tensors. We introduce a alternative embedding of the tensor product space into a projective space.…
We determine the crossover exponents associated with the traceless tensorial quadratic field, the third- and fourth-harmonic operators for O(n) vector models by re-analyzing the existing six-loop fixed dimension series with pseudo-epsilon…
We construct the quaternion algebra [10] "geometrically" by a three dimensional analogue of the classic two dimensional geometric description of the complex field. The algebraic description of the multiplication operation in three…
Cartesian harmonic tensors are completely symmetric traceless tensors in three dimensional space constructed from the direct product of unit vectors. They are useful in generating expressions for the angular coupling of spherical harmonics…
We study orthogonal decompositions of symmetric and ordinary tensors using methods from linear algebra. For the field of real numbers we show that the sets of decomposable tensors can be defined be equations of degree 2. This gives a new…
We present an extension of the tensor grid method for stray field computation on rectangular domains that incorporates higher-order basis functions. Both the magnetization and the resulting magnetic field are represented using higher-order…
It is shown that the SO(3) isometries of the Euclidean Taub-NUT space combine a linear three-dimensional representation with one induced by a SO(2) subgroup, giving the transformation law of the fourth coordinate under rotations. This…
Tensor harmonics are a useful mathematical tool for finding solutions to differential equations which transform under a particular representation of the rotation group $\mathrm{SO}(3)$. The aim of this work is to make use of this tool also…
Higher-order tensors appear in various areas of mechanics as well as physics, medicine or earth sciences. As these tensors are highly complex, most are not well understood. Thus, the analysis and the visualization process form a highly…
We present a method for designing smooth cross fields on surfaces that automatically align to sharp features of an underlying geometry. Our approach introduces a novel class of energies based on a representation of cross fields in the…
Tensor train decomposition is widely used in machine learning and quantum physics due to its concise representation of high-dimensional tensors, overcoming the curse of dimensionality. Cross approximation-originally developed for…
Our previous work [1] constructed, in three-dimensional momentum space, a manifestly crossing symmetric basis for scalar conformal four-point functions, based on the factorization property proposed by Polyakov. This work extends this…
Contemporary presentation of the version 1 demonstrates briefly the development of our investigations and our future goals. The improved free of difficulties in interpretation and printing errors version is presented. The 256-dimensional…
In a attempt to treat a supergravity as a tensor representation, the 4-dimensional N-extended quaternionic superspaces are constructed from the (diffeomorphyc)graded extension of the ordinary Penrose-twistor formulation, performed in a…
In this paper we introduce an intermediate field representation for random matrices and random tensors with positive (stable) interactions of degree higher than 4. This representation respects the symmetry axis responsible for positivity.…